Preheat oven to 350 degrees F. Butter and flour a 5- by 9-inch loaf pan. In a medium bowl, whisk together flour, baking soda, and salt.

In a large bowl, using an electric mixer, beat butter and sugar on medium-high until fluffy, 3 minutes. Add eggs, one at a time, beating well after each addition and scraping down bowl as needed. Beat in bananas, sour cream, and vanilla. Beat in flour mixture and chocolate on medium. Pour batter into pan. Bake until a skewer inserted in center of loaf comes out clean, 50 to 60 minutes.